High-temperature specific heat of crystals

Abstract

The Monte Carlo method is used to estimate the specific heat of a model of rubidium. Both the specific heat at constant volume, $C_{\nu }$, and the specific heat at constant pressure, $C_p$, are obtained for a range of temperatures up to the instability point of this lattice. These results for the fully anharmonic perfect crystal are compared with those obtained by perturbation theory to lowest order in the anharmonicity, (i.e., only cubic and quartic anharmonic contributions to the Helmholtz free energy are considered). It is shown that the fully anharmonic Monte Carlo calculation yields a more rapidly increasing specific heat than the linear temperature dependence given by lowest-order perturbation theory in the high-temperature limit. The Monte Carlo calculations also indicate that, at temperatures much higher than the Debye temperature, large-scale atomic displacements can occur without disrupting the lattice. When this happens, there is a further increase in the specific heat.